impression test—a review

Materials Science and Engineering R xxx (2013) xxx–xxx

G Model

MSR-431; No. of Pages 21

Impression test—A review

Fuqian Yang a, James C.M. Li b,*a Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506, USAb Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.1. Analysis of indentation deformation of materials by a cylindrical punch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.2. Impression of linearly elastic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.3. Impression of plastic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.4. Impression creep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.4.1. Stress-induced diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.4.2. Dislocation creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.5. Viscous flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1.6. Contact adhesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2. Impression method as a technique for mechanical testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.1. Comparison of creep curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.2. Comparison with conventional creep tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.3. Comparison with conventional tensile or compression tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.4. Comparison with double shear creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.5. Anisotropic creep behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.6. Diffusional creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.7. Dislocation creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.8. Stress relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.9. Superplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.10. Viscosity measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.11. Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.12. Impression adhesion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.13. Impression Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.14. Testing of solder ball grid array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.15. Nondestructive testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.16. Time to reach steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2.17. A word on indentation creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3. Materials tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.1. Aluminum alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.2. Copper alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.3. Lead alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

A R T I C L E I N F O

Article history:

Available online xxx

Keywords:

Impression test

indentation test

creep

load-displacement relation

A B S T R A C T

Indentation test using a cylindrical indenter with a flat end is now known as impression test. The

advantage is its capability to reach a steady state for creep test at constant load and it is possible to

compare with the conventional tensile or compression tests. The test is simple and all the temperature

and strain rate dependences can be obtained locally from one sample avoiding the sample to sample

variations. It became very popular in the last decade. The literature is reviewed here.

� 2013 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

Materials Science and Engineering R

jou r nal h o mep ag e: w ww .e lsev ier . co m / loc ate /m ser

* Corresponding author.

E-mail address: [email protected] (James C.M. Li).

Please cite this article in press as: F. Yang, J.C.M. Li, Mater. Sci. Eng. R (2013), http://dx.doi.org/10.1016/j.mser.2013.06.002

0927-796X/$ – see front matter � 2013 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.mser.2013.06.002


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F. Yang, J.C.M. Li / Materials Science and Engineering R xxx (2013) xxx–xxx2

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3.4. Magnesium alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.5. MoSi2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.6. Nanocrystalline materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.7. Ni alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.8. Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.9. Power plant materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.10. SiAlON ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.11. Stainless steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.12. Thermal barrier coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.13. Thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.14. Tin-based solders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.15. Titanium aluminide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.16. Uranium alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.17. Weldments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.18. Zircaloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.19. Zn alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3.20. Closure remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

1. Introduction

Ever since we started using a cylindrical punch to doindentation test locally and measuring the steady state penetrationvelocity as a function of time, see Chu and Li [28], it is now a useful‘‘impression test’’ to replace the costly and time consuming creeptests. For a recent review, see Li [93]. Many more papers have beenpublished since then. Most of them will be summarized here.

Indentation creep was reviewed recently by Goodall and Clyne[59] and Choi et al. [24].

The impression test has two distinctive features compared tothe sharp-instrumented indentation test, which are

(1) the punch is of cylindrical shape with a flat end instead ofspherical, conical, or pyramidal shape;

(2) at constant load, the average contact stress is constant and theplastic zone underneath the punch will be developed to aconstant size so that the plastic deformation is associated withthe propagation of the plastic zone.

One of the challenges for the applications of the impression testat the small scale is the fabrication of flat-ended indenters of smallsize. Using focused ion beam milling, Cross et al. [32] successfullyfabricated a flat-ended indenter of 2 mm diameter from a Si-sphereof 1 mm diameter and Rowland et al. [143] made a flat-endedindenter of 1.6 mm diameter as shown in Fig. 1. Their approachdemonstrated the possibility of fabricating flat-ended indenters ofsmall size by using focused ion beam milling. It provides therationale of using nanofabrication techniques, such as FIB andnanolithography, to fabricate flat-ended indenters from nanos-tructures including nanowires and nanorods. In addition, nano-tubes can also be used to make nano-annular indenters of flat endfor the impression test of nanostructure materials, as Yang and Li[181] discussed the feasibility of using a flat-ended, annularindenter in characterizing the impression behavior of materials.The fabrication of flat-ended indenters of small size is the key forapplying the impression test in nanostructures and nanomaterials.

Similar to the sharp-instrumented indentation test, theimpression test has significant advantages over conventionalmechanical tests of tension, compression, shear and etc. Theseadvantages include small specimen volume, constant stress atconstant load, and the capability to characterize local mechanicalproperties of heterogeneous materials, such as grain boundariesand interfaces. In contrast to the indentation test by a sharpindenter, careful alignment between the flat surface of a punch andthe specimen surface is needed to limit the effect of the punch tilton the measurement. Due to the complex stress field underneath

Please cite this article in press as: F. Yang, J.C.M. Li, Mater. Sci. Eng.

the punch, one needs to establish analytical or semi-analyticalrelationships between the impression test and the conventionalmechanical tests in order to use the impression test to characterizethe mechanical properties of materials of small volume.

1.1. Analysis of indentation deformation of materials by a cylindrical

punch

Fig. 2 schematically shows the contact between a rigid,cylindrical punch and a material of thickness h on a rigid substrate.There are two limiting contact conditions between the punch andthe material at the contact interface. One is frictionless as used byBoussinesq [10] and Sneddon [153] and the other is non-slip asused by Galin [43] and Spence [154] for the contact of an elastichalf-space. Similarly, there are two limiting contact conditions atthe interface between the material and the rigid substrate; one isfrictionless and the other is non-slip (perfect bonding). The appliedforce to the punch can be calculated from the integration of thenormal stress over the contact zone.

1.2. Impression of linearly elastic materials

The contact problem between an elastic half-space and a rigid,cylindrical punch of radius a is related to Boussinesq [10] contactproblem. For the frictionless contact between the half-space andthe punch, the normal stress distribution over the contact zone canbe found as

sn ¼ � E

1 � n2

dp

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 � r2p (1)

which gives the force, F, applied to the punch as

F ¼ 2Ead1 � n2

(2)

Here, sn is the normal stress on the contact interface, E and v areYoung’s modulus and Poisson’s ratio of the material, respectively,and d is the displacement of the punch.

For the non-slip contact, the applied force [154,188] is

Fs ¼2Ead

1 � n2

ð1 þ nÞlnð3 � 4nÞ1 � 2n

(3)

The ratio of F/Fs is larger than unity as expected for the samepunch displacement. For incompressible elastic materials, i.e.v = 0.5, Eq. (2) is identical to Eq. (3). The contact condition has noeffect on the elastic contact of incompressible, semi-infinite elasticmaterials.

R (2013), http://dx.doi.org/10.1016/j.mser.2013.06.002


Fig. 2. Schematic of the impression test.

Fig. 1. A flat-ended indenter of 1.6 mm diameter, made from a Si-sphere of 1 mm

diameter by focused ion beam milling. Reprinted with permission from [143].

Copyright [2008], American Chemical Society.

F. Yang, J.C.M. Li / Materials Science and Engineering R xxx (2013) xxx–xxx 3

G Model


King [82] conducted numerical analysis for the impression of anelastic half-space by rigid, flat-ended punches of cylindrical,triangular, and square cross sections with frictionless contactcondition. He obtained

F ¼ 2Ead1 � n2

x (4)

where x = 1 for the cylindrical punch, x = 1.01 for the squarepunch, and x = 1.03 for the triangular punch.

From Eqs. (2) and (3), the contact stiffness S can be calculated as

S ¼ dF

dd¼

2Ea

1 � n2frictionless contact

2Ea

1 � n2

ð1 þ nÞlnð3 � 4nÞ1 � 2n

non-slip contact

8><>: (5)

The contact stiffness is proportional to the punch radius andindependent of the punch displacement. Obviously, both Young’smodulus and Poisson’s ratio can be determined from the unloadingcurves of the impression tests if one can control the contactcondition between the punch and the material surface.

For the contact between an ultra-thin film and a rigid,cylindrical punch, the applied force to the punch is dependenton the contact condition between the punch and the film and thatbetween the film and the rigid substrate. There are fourcombinations for the limiting frictionless or non-slip contactcondition: case (I) frictionless on all contact faces, case (II)frictionless on the interface between the punch and the film andnon-slip between the film and the substrate, case (III) non-slipbetween the punch and the film and frictionless on the interfacebetween the film and the substrate, and case (IV) non-slip on all thecontact faces.

The relationship between the applied force and the punchdisplacement for the indentation of an incompressible elastic filmwith the contact radius much larger than the film thickness of h

ða � hÞ is [172]

F ¼

4pma2dh

case Ið Þ3pma4d

8h3case IIð Þ and IIIð Þ

3pma4d

2h3case IVð Þ

8>>>>>><>>>>>>:

(6)


where m is the shear modulus of the film. In contrast to theindentation of an incompressible elastic half-space, the applied forceis a nonlinear function of the punch radius and is dependent on thefilm thickness. From Eq. (6), the contact stiffness is found to be

S ¼

4pma2

hcase Ið Þ

3pma4

8h3case IIð Þ and IIIð Þ

3pma4

2h3case IVð Þ

8>>>>>><>>>>>>:

(7)

which is independent of the punch displacement.For the indentation of a compressible elastic film with the

contact radius much larger than the film thickness and frictionlesscontact between the punch and the film, the relationship betweenthe applied force and the punch displacement is [174,175]

F ¼

pEa2dð1 � n2Þh case Ið Þ

ð1 � nÞpEa2dð1 þ nÞð1 � 2nÞh case IIð Þ

8>><>>: (8)

which gives the contact stiffness as

S ¼

pEa2

ð1 � n2Þh case Ið Þ

ð1 � nÞpEa2

ð1 þ nÞð1 � 2nÞh case IIð Þ

8>><>>: (9)

In contrast to the indentation of an incompressible elastic film,both the applied force and the contact stiffness are proportional tothe square of the punch radius, independent of the contactcondition between the film and the substrate.

Various models have been proposed to study the effect ofdeformable substrate on the reduced contact modulus and toextract the reduced contact modulus of multilayer structure fromthe indentation loading-unloading curves. Doerner and Nix [35]approximated the indentation of a bilayer structure as a series ofsprings and developed an empirical relation among the effectivereduced contact modulus and the elastic moduli of film andsubstrate, in which a curve fitting of experimental data is needed todetermine a parameter. King [82] analyzed the problems of flat-ended cylindrical, quadrilateral, and triangular punches indentinga layered isotropic elastic half-space and proposed a semi-analytical relationship describing the contact stiffness as afunction of the ratio of the film thickness to the contact sizeand the material properties of the layered structure. Gao et al. [42]used the variation method to develop a semi-analytical solution forthe contact between a rigid flat-ended indenter and an elastic layer



0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100

Mea

n i

ndenta

tion

pre

ssure

/y

2a (µm)

Exper imental data

Fig. 3. Variation of the mean indentation pressure with the punch size for the

impression of the compression-molded high impact polystyrene. The experimental

result is for the impression by a cylindrical punch of 72 mm diameter. Reprinted

with permission from [99]. Copyright [2008], Institute of Physics.


G Model


adherent to an elastic half-space. They neglected the contributionof the variation in the displacement field to the energy change.Based on a macroscopic coating-substrate system, Hsueh andMiranda [61] extended the Hertizan contact theory to the contactof multilayer structure and established a relation between theindentation depth and the elastic modulus of each layer. Based onHsueh and Miranda [61] result, Geng et al. [44] established a semi-empirical relation for calculating the reduced contact modulus ofthe polymeric coating.

1.3. Impression of plastic materials

Kirsch [83] was the first to propose the use of a cylindricalpunch to study the hardness of metals. In general, it is very difficultto establish an analytical relationship between indentationhardness and yield stress. Two techniques have been developedto analyze the indentation deformation of plastic materials; one isthe elastic–plastic cavity expansion model [9,160] and the other isthe slip-line limit method for perfectly plastic materials [149].

Using the slip-line limit method, Shield [149] analyzed theimpression of a semi-infinite body of perfectly plastic material by arigid, frictionless, cylindrical punch of flat end. A lower bound forthe indentation hardness was found to be 5.69ty, i.e.

H ¼ F

pa2� 5:69ty ¼ 2:845sy (10)

Here H is the indentation hardness and ty is the shear yieldstress. The slip-line field given by Shield [149] showed that theprincipal stress varies in the range of 5.142–7.2ty.

Johnson and Mellor [70] analyzed the impression of a semi-infinite block of perfectly plastic material by a flat, rigid,frictionless, rectangular punch and found that a lower bound tothe contact pressure is 5ty. Shield and Drucker [150] investigatedsimilar problem by a flat, rigid, frictionless, square punch andobtained H = 5.71ty. Thus, Johnson and Mellor [70] found:

5 <H

ty< 5:71 or

H

ty¼ 5:35 � 7% (11)

for a square punch.For the impression of elastic-plastic materials, there is no

analytical relationship between the indentation hardness and theyield stress of the materials. Both experimental and numericalwork have found that the indentation hardness is proportional tothe yield strength of the materials determined from the uniaxialtests as [99,193,195]

H ¼ asy (12)

where a is a constant dependent on the material properties and theratio of the elastic modulus to the yield stress [99].

For plastic materials with a power-law relationship betweentrue stress, st, and true strain, et, as

st ¼ bent (13)

where b is a constant and n is the strain-hardening exponent. Yuet al. [193] suggested that the indentation hardness as a function ofthe punch displacement can be expressed as

H ¼ lb d2a

� �n(14)

with l being a proportional constant. It is noted that bothnumerical simulation and experimental study are needed toconfirm Eq. (14).

Due to the complexity of the contact deformation, finiteelement method has been used to analyze the deformationbehavior of elastic-plastic materials. Riccardi and Montanari[139] performed finite element analysis of the impression of an


elastic-perfectly-plastic material and found that the ratio of theindentation hardness to the tensile yield stress is approximatelyequal to 3 for the frictional contact with the friction coefficient inthe range of 0 to 0.5. They also showed that the ratio increases withthe increase of the strain-hardening exponent.

Lu et al. [99] used finite element method to analyze theimpression of elastic–plastic materials with strain hardening. Thesimulation results showed that the indentation hardness isproportional to the punch displacement at large indentationdepth, from which one can calculate the average indentationpressure at the onset of yielding. Fig. 3 shows the dependence ofthe average indentation pressure on the punch diameter for theimpression of the compression-molded high impact polystyrene. Itis interesting to note that the average indentation pressuredecreases slightly with increasing the punch size, which isqualitatively in accord with Eq. (14). This result suggests thatthere is a size dependence of the indentation hardness for theimpression of elastic-plastic materials with strain hardening.

1.4. Impression creep

1.4.1. Stress-induced diffusion

There are several rate controlling mechanisms for the creepdeformation of materials, such as lattice diffusion, grain boundarydiffusion, grain boundary sliding, grain boundary flow, anddislocation creep over a range of stresses and temperatures. Inthe stress-induced diffusion, the vacancy diffusion is not caused by auniform stress since a vacancy cannot migrate without exchangingits position with a nearby atom in a crystal [182] and this exchangemay not be affected by a stress. However, vacancies can be created orremoved at any interface and when this interface is stressed, thechemical potential of a vacancy is affected. So when the surfaces orinterfaces are stressed differently, the equilibrium concentration ofvacancies will be different for different surfaces or interfaces. Atomswill then migrate from one interface to another and a flow occursresulting in a shape change of the crystal.

The local equilibrium concentration of vacancies for steadystate vacancy flow starting from the free surface and endingunderneath the punch will be maintained mechanically by thelocal normal stress on the contact zone as

snV ¼ RTlnc0c (15)




G Model


where V is the molar volume of the diffusion species, c is theconcentration of vacancy (moles per unit volume), c0 is theequilibrium concentration of vacancy at larger distances fromthe contact zone where the stress is zero, R is the gas constant, andT is absolute temperature.

For the lattice diffusion-limited impression creep of a layer ofmaterial by a rigid, cylindrical punch, the relationship between thepenetration velocity and the force applied to the punch is, [178]

V ¼ 1

f� pDV2

c0

RT

F

pa2(16)

with

f ¼4a=3 half spacepa2=8h impermeable substrate ða � hÞph permeable substrate ða � hÞ

8<: (17)

here V is the penetration velocity of the punch and D is thediffusivity of vacancy.

It is known that vacancies can migrate either through thecrystal or along the interface between the punch and the crystalduring the penetration of the punch. The interface diffusion-limited impression creep was first studied by Chu and Li [28]. Themechanism is different from lattice diffusion and involvesinterface diffusivity of vacancies. Chu and Li [28] gave arelationship between the penetration velocity V and the forceapplied to the punch F as

V ¼ 8DsV2cso

RTa2

F

pa2(18)

for the impression creep by a rigid, cylindrical punch of radius a.Here, Ds is the interface diffusivity of vacancies and cso is theconcentration of vacancy at the boundary of the contact zone.

For the interface diffusion-limited impression creep, thepenetration velocity is,

V ¼ 12; 960

11� DsV

2cso

RTb2

4Fffiffiffi3p

b2(19)

for a punch of equilateral triangle of side b, and

V ¼ p4

128� DsV

2cso

RTa2

F

ab

X1i¼1;3;5

1

i41 � 2a

ipbtanh

ipb

2a

� �24

35�1

(20)

for a punch of rectangular cross-section of 2a � 2b.

1.4.2. Dislocation creep

Dislocations can be generated during impression creep andtheir motion contributes to the creep deformation of a material.The power flow rule describing the deformation process in onedimension can be expressed as

e ¼ Asm (21)

where m is the stress exponent. Using the effective stress, one canobtain the corresponding constitutive relationship in three-dimensions.

Using finite element method [65,68,157,192], it has beenshown that the steady state penetration velocity for impressioncreep is proportional to the diameter of the punch and the relationbetween the steady state penetration velocity and the averagestress applied to the punch obeys the same power-law as inuniaxial creep.

Considering the effect of surface cavity and the non-slip/frictionless contact conditions, Yang [173] performed finiteelement analysis of the impression creep of a semi-infinitematerial by using the 1D constitutive relation of Eq. (21). Ingeneral, the steady state penetration velocity can be expressed as


[173]

V ¼ 2aAcðm; L=aÞ F

pa2

� �m

(22)

where c(m, L/a) is a function of m and L/a (L is the depth of cavity).c(m, L/a) approaches a constant for m > 4 and L/a = 1, whichdepends on the contact condition at the interface between thepunch and the material. For L/a = 1, the finite element resultsshowed that c(m, L/a) can be expressed as

½cðm; L=aÞ��1=m

¼

3:83 þ 0:18m�1 � 2:14m�2 all slip

4:15 � 0:25m�1 � 1:97m�2 bottom stick

5:6 þ 2:3m�1 � 10m�2 þ 4:3m�3 stick on lateral surface

5:7 þ 1:8m�1 � 8:8m�2 þ 3:6m�3 all stick

8>>><>>>:

(23)

Obviously, the conversion factor between the impression creepand the conventional creep depends on the stress exponent m.

Based on experimental results for the impression creep andrelaxation of Pb–Sn eutectic alloy, Yang et al. [186] simulated theimpression creep of an elastic-plastic material obeying the Eyringhyperbolic sine flow law,

e ¼ sEþ AsinhðBsÞ (24)

They found that, if the average indentation pressure is dividedby a factor of 3.5, the steady state penetration velocity is also ahyperbolic sine function of the applied force as

V ¼ 3p8

aAð3:5ÞsinhB

3:5� F

pa2

� �(25)

here B is a constant proportional to the molar volume of thematerial.

1.5. Viscous flow

There are many ways to measure high viscosity (>106 Pa s),such as torsion, tension, compression, bending, and indentation.In the indentation techniques, a cylindrical punch of flat end ispreferable to a conical or spherical indenter because steadyviscous flow can be achieved at constant load. In fact onlycylindrical punches of flat end can produce a steady stateimpression velocity.

For the impression of a semi-infinite viscous medium, therelation between the applied force F and the steady-statepenetration velocity V is [183]

V ¼ pa

8h� F

pa2(26)

which is independent of the contact condition (slip/non-slip) at theinterface between the punch and the surface of the viscousmedium. Here h is the viscosity of the viscous medium. Thepenetration velocity is inversely proportional to the punch radiusfor the same applied force.

For the impression of a thin viscous layer of thickness h with thepunch radius much larger than the film thickness, the relationshipbetween the applied force and the penetration velocity is [14]

V ¼ 2h3

3a2h� F

pa2(27)

for non-slip contact and zero pressure at the contact edge,

V ¼ h

2h� F

pa2(28)



Fig. 4. Comparison of the creep curves for pure tin; (a) tensile creep, (b) impression

creep. Reprinted with permission from [29]. Copyright [1979], Elsevier, and (c)

indentation creep. Reprinted with permission from [148]. Copyright [2012], Elsevier.


G Model


for perfect slip contact and zero pressure at the contact edge, and

V ¼ h

3h� F

pa2(29)

for perfect slip contact and zero normal stress at the contact edge.

1.6. Contact adhesion

Knowledge of contact adhesion between solids is important inunderstanding the mechanisms of the sticking behavior of micro-and nano-mechanical structures. Shull [152] reviewed the contactadhesion of soft solids with the focus on the JRK model. Kendall[77] studied the contact adhesion between a rigid, cylindricalpunch and a semi-infinite elastic medium, which can overcome thecontact hysteresis during the JKR contact. Without any pre-existing interfacial crack, the contact adhesion between a rigid,flat-ended punch and a semi-infinite elastic medium can bemeasured from the pull-off force, Fpull-off, as [77]

Fpull-off ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi8pEa3g1 � n2

r(30)

for frictionless contact. Here, g is the interfacial energy betweenthe flat-ended punch and the semi-infinite elastic medium. Eq. (30)reduces to

Fpull-off ¼ 4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pma3g

q(31)

for an incompressible elastic half-space [187]. Eq. (31) has beenverified in studying the self-adhesion of PDMS [poly(dimethylsi-loxane)] [187].

Using reversible thermodynamics and the elastic solution of thecontact between a rigid, cylindrical punch and an incompressibleelastic thin film with h � a, the pull-off force to separate the punchfrom the elastic thin film is found to be [187],

Fpull-off ¼ 2pa2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mg=h

q(32)

for frictionless contact at both contact interfaces,

Fpull-off ¼pa3

2h

ffiffiffiffiffiffiffiffiffiffi3mg2h

r(33)

for frictionless contact between the punch and the elastic film andnon-slip between the elastic film and the substrate or non-slipbetween the punch and the elastic film and frictionless contactbetween the elastic film and the substrate, and

Fpull-off ¼pa3

h

ffiffiffiffiffiffiffiffiffiffi3mg2h

r(34)

for non-slip at both contact interfaces.For adhesive contact between a compressible elastic film and a

rigid, cylindrical punch with h � a, there are

Fpull-off ¼ 2pa2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEg

2hð1 � n2Þ

s(35)

for frictionless contact at both contact interfaces [174], and

Fpull-off ¼ pa2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ð1 � nÞEg

hð1 þ nÞð1 � 2nÞ

s(36)

for frictionless contact between the punch and the elastic film andnon-slip between the elastic film and the substrate [175].


2. Impression method as a technique for mechanical testing

2.1. Comparison of creep curves

It has been common to observe the creep deformation inindentation experiments. This observation has stimulated theinterest to use indentation test to characterize the creep propertiesof materials [118,119,148,197]. Most of the methods used in




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analyzing the indentation creep have used the power-lawrelationship between the indentation stress and the penetrationrate to determine the stress exponent or activation energy, eventhough no explicit assumption of steady state creep has been usedin the analysis. The use of the power law relationship for theindentation creep with an indenter of non-flat end is questionable,since the contact area increases with the increase of indentationdepth, resulting in the decrease of the contact stress. Theindentation creep actually is at non-steady state, and the timeeffect needs to be incorporated in the analysis. Simple use of the

Fig. 5. Comparison of the creep curves for Pb-Sn eutectic alloy; (a) double shear

creep. Reprinted with permission from [120]. Copyright [1990], Springer, (b)

impression creep. Reprinted with permission from [71]. Copyright [1986], Springer,

and indentation creep. Reprinted with permission from [41]. Copyright [2001],

Elsevier.


power law relation likely is not enough to represent thecharacteristics of the indentation creep.

Fig. 4 shows the creep curves for pure tin under three testingconditions: (a) tensile creep test, (b) impression creep test, and (c)indentation creep test. For the tensile creep shown in Fig. 4a, thedeformation of tin showed the usual three stages: (a) transientstage, (b) steady state stage, and (c) tertiary stage. In the steadystate stage, the strain rate is constant with time but varies withstress and temperature. Similar to the tensile creep teat, theimpression creep of tin shown in Fig. 4b shows two stages, atransient stage and a steady state stage in which the penetrationrate is constant. This penetration rate can be related to the steadystate tensile strain rate by a conversion factor. In contrast to thetensile creep and impression creep of tin, there is no steady state inthe indentation creep by using the Berkovich indenter, as shown inFig. 4c. Thus, the impression creep provides a method capable ofinvestigating localized steady state creep of materials.

Fig. 5 shows a comparison of creep curves for the Pb–Sn eutecticalloy under three testing conditions: (a) double-shear creep test,(b) impression creep test, and (c) indentation creep test. Onceagain, the impression creep curves of Pb–Sn eutectic alloyresemble those of the double shear creep with steady-state creep.There is no steady state for the indentation creep of Pb–Sn eutecticalloy by using a conical indenter, as shown in Fig. 5c.

Note that the indentation depth vs. time curves generally arenot very useful for analyzing indentation creep. It would be betterto analyze the penetration rate vs. the indenting stress, since boththe penetration rate and the indenting stress change with time. Thechallenging issues are: (1) the determination of the actual contactarea since there is no good approach to measure the contact area inreal time, and (2) the lack of a reasonable correlation between thepenetration rate and the indenting stress for time-dependentindentation creep.

2.2. Comparison with conventional creep tests

From the very beginning we compared the impression creeptests with conventional creep tests and obtained agreement inboth the stress exponent and activation energy, see Chu and Li[28,29]. Later there have been many comparisons reported seerecent review [93]. Yang [173] studied the effect of slip, stick andcavity depth on the impression velocity by using finite elementmethod. His conclusions are (1) the stress exponent betweenimpression velocity and punching stress is the same as the power

Fig. 6. Variation of the impression depth with time for the impression creep of lead.

Reprinted with permission from [21]. Copyright [1994], Cambridge University

Press.



Fig. 7. Dependence of the steady state impression velocity on punching stress for the impression creep of lead. Reprinted with permission from [21]. Copyright [1994],

Cambridge University Press.


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law exponent assumed in the calculation, (2) the maximum vonMises stress under the punch is proportional to the applied loadand dependent on the stick or slip conditions between the punchand the material, (3) the punch penetration showed a constantvelocity after a transient stage which increased with the powerexponent and decreased with the cavity depth, and (4) for the sameapplied load, the steady state impression velocity is the largest forall slip conditions and smallest for all stick conditions.

Chiang and Li [21] compared impression creep of single crystallead with conventional creep reported in literature. Fig. 6 showsthe variation of the impression depth with time. After a shorttransient stage, the impression creep reached a steady state with aconstant impression velocity. Fig. 7 shows the stress dependence ofthe steady-state impression velocity for lead, from which the stressexponent was calculated. The stress exponent values are in therange of 3.5 � 0.5 at 563 K to 8.0 � 0.8 at 296 K, depending ontemperature. Fig. 8 shows the temperature dependence of the steady-state impression velocity for lead. The activation energy is generallyhigher in the low stress region and lower in the high stress region.Both the temperature and stress dependences are comparable to

Fig. 8. Dependence of the steady state impression velocity on temperature for the

impression creep of lead. Reprinted with permission from [21]. Copyright [1994],

Cambridge University Press.


those of constant stress tensile creep. Fig. 9 is a master curve for thecreep deformation of lead, which can be used to analyze the creepdeformation of lead and to predict the life time of mechanicalstructures made of lead at high temperatures.

Sastry [146] compared impression creep and tensile creep of Mgby dividing the impression velocity by the diameter of the punch tocompare with the tensile strain rate and by dividing the punchingstress by 3 to compare with the tensile stress, as suggested by Chuand Li [28]. The plot of strain rate versus stress showed a single line

Fig. 9. Master curve for the creep of lead. Reprinted with permission from [21].

Copyright [1994], Cambridge University Press.



Fig. 10. A typical true stress against normalized penetration curve of Al obtained by

an impression. Reprinted with permission from [193]. Copyright [1985], Springer.


G Model


for both tests at 478 K. The same comparison was made for Cd at373, 403 and 433 K. The stress exponent was 5.7 for Cd in thetemperature range of 368 to 453 K for impression creep. For tensilecreep, they were 5.2 to 5.7 in the temperature range of 348 to433 K. The stress exponent for Zn at 373 K was 4.5 to 4.6 forimpression creep and 4.0 to 4.5 for tensile creep. The stressexponent for superplastic Zn-22 wt%Al alloy and a near eutecticSn–Pb alloy by using impression creep also agreed with those inthe literature from conventional creep tests.

Hsueh et al. [62] derived a close form solution for the case of n = 1(stress exponent) and compared with the finite element solution.Then they used finite element analysis for cases of large n. Theirimproved correlations agreed with those given by Hyde et al. [68].

Fox et al. [40] compared impression and compression creeps ofYb–SiAlON ceramics. See below for details. The stress exponent forimpression creep was about 2 but that for compression creep wasonly about 1. The average activation energy for impression creepwas 562 kJ/mol and that for compression creep was 487 kJ/mol.The difference could be due to the different stresses applied.

Park et al. [134] compared impression creep of polycrystallineSn to compression creep of the same material. They foundagreement for the stress component (about 5) and the activationenergy (about 42 kJ/mol). If the impression velocity divided by thediameter of the punch was C times the uniaxial strain rate, and ifthe punching stress was the uniaxial stress multiplied by k, theyfound the factor k/C to be 941 experimentally in agreement withtheir own finite element simulation which yielded 910. Thisnumber would be 482 using k = 3.33 and C = 0.84 as suggested byChu and Li [28] or it would be 584 using k = 3.38 and C = 0.755 assuggested by Hyde et al. [68]. See later in Section 2.7.

Hyde and Sun [64] reported the variation of parameters whichconverts the punching stress to tensile stress or the impressionvelocity to strain rate by using finite element simulation. They usedindenters of rectangular cross sections.

More recently Yang et al. [169] compared impression creepwith uniaxial tensile creep of Ni-based single crystal superalloys bycomputer simulation. Three orientations of [0 0 1], [0 1 1] and[1 1 1] were tested. The stress exponents obtained were 4.96, 5.13and 5.10, respectively for impression creep and 5.13, 5.10 and 5.12for uniaxial tensile creep. These results were from finite elementcalculations. It is noted here that impression creep and uniaxialtensile creep are two different tests. Only the stress exponent andactivation energy should be compared.

Cseh et al. [31] compared impression creep with indentationcreep by a hemispherical punch for lead glass, aluminum andAlSi12CuMgNi (M124) alloy. They suggested that the hemispheri-cal punch was also suitable for the determination of time-dependent plastic deformation of materials.

For a recent review see Hyde et al. [67].

2.3. Comparison with conventional tensile or compression tests

Yu et al. [193] used impression test at room temperature at aconstant penetration rate of the punch to compare with conven-tional compression test. Fig. 10 shows a typical true stress againstnormalized penetration curve of Al obtained by an impression.When they plotted the average contact stress against the depth ofpenetration divided by the punch diameter, it showed the elasticregion, yielding and work hardening. When they compared with thecompression stress–strain curve for 1018 steel, Al, Cu and Ni, theaverage contact stress was higher than the compressive stress by aconstant factor. Similarly the penetration depth divided by thediameter of the punch was smaller than the compressive strain by aconstant factor. By using these two factors, the stress–strain curvesgenerated by the impression test and the compression test were verysimilar to each other. Independent of these factors the work


hardening exponent could be obtained by plotting the averagecontact stress vs. penetration depth on a log–log scale.

For the impression test, Yu et al. [193] found good agreementfor the elastic moduli of 1018 steel, Al, Cu and Ni as compared withthe compression test (shown in Fig. 11) similar to the case ofspherical indenters.

Ferranti et al. [38] used a spherical indenter to determine theelastic behavior of solid and porous Al during the loading phase.The elastic modulus obtained for solid Al was 67.8 � 6.6 GPa inagreement with a handbook value of 72.4 GPa for 2024 Al. For theporous Al pellet (3.3% porosity), the elastic modulus was22.6 � 4.5 GPa. For the H-12 grade porous pellet of slightly lowerdensity (95.8% dense), the elastic modulus found was 24.5 � 3.8 GPa.

Montanari and co-workers [33,55–57,140] have used impressiontest to characterize mechanical properties of various metals andalloys with the focus on time-independent plasticity and elasticmodulus. Riccardi and Montanari [139] summarized their results forvarious materials, including Al, Cu, steel etc. They suggested thatimpression test is a good technique to characterize yield stress andelastic modulus of metals. Also, it is possible to determine theductile-to-brittle transition temperature for some alloys.

Kumar et al. [87] evaluated the effect of the displacement rateon the impression behavior of an Al foam. The indentation load-displacement response was similar to that under uniaxialcompression. There was linear dependence of the plastic collapsestrength on the indentation displacement rate, the same as that foruniaxial compression; the plastic collapse strength obtained fromthe impression test was larger than that from the compression test,possibly reflecting the effect of shearing cell walls.

Lu et al. [98] studied the impression deformation of Al foams.They suggested that the total indentation load consisted of thecontributions from the crushing of the foam and the tearing of thecell walls. The indentation load-displacement curve was similar tothat for the compression test of the specimen of the same diameter,while there are various zig-zag events in the loading curve possiblyrepresenting the tearing of the cell walls and the load for the samedisplacement generally was larger than that for the compressiontest. The tear energy was 15.6 kJ/m2 for Al foam with a nominalrelative density 10%.

2.4. Comparison with double shear creep

Kim [81] compared the impression creep of AZ31 Mg alloy withthe double shear creep in the temperature range of 423 to 473 K.



Fig. 11. A plot of compression against impression tests for elastic moduli showing a

linear relationship. Reprinted with permission from [193]. Copyright [1985],

Springer.


G Model


The punch diameter was 1.0 mm, and the sample thickness was3 mm. Both creep tests gave the same stress exponent of 3.5 forlow stresses and activation energy of 109.1 kJ/mol. For highstresses, the stress exponent was 6.7. He suggested that viscousglide is the rate-process for the creep of the AZ31 Mg alloy andcalculated the pre-exponential constants to correlate the impres-sion creep with the double shear creep. However, one must realizethat the conversion factors between the double shear creep and theimpression creep is dependent on the ratio of the punch size to thesample thickness for the impression test. Numerical analysis isneeded to establish a more general relationship.

2.5. Anisotropic creep behavior

Chu and Li [29] examined the impression creep of b-tin in threeorientations: [0 0 1], [1 0 0 0], and [1 1 0]. The activation enthalpywas stress-dependent for low temperature process, which are8.2 kcal/mol for the [0 0 1] orientation at 16–20 MPa, 10 kcal/molfor [0 0 1] at 12–16 MPa and 9.4 kcal/mol for [1 1 0] at 16–20 MPa.The stress dependence of the impression velocity obeyed a powerlaw with stress exponents between 3.6 and 5.0, in generalagreement with previously reported results from conventionalcreep tests.

Godavarti and Murty [50] showed anisotropic impression creepbehavior on large grained Zn using a cylindrical WC indenter of1.587 mm diameter. The impressing rate was different for threeadjacent faces. The stress exponent was 3.4 for one face and 4.4 foranother. However the activation energies were similar for the threefaces, 82 � 5 kJ/mol at high temperatures and 58 � 8 kJ/mol at lowtemperatures in the range of 398 and 498 K.

2.6. Diffusional creep

Chu and Li [28] analyzed diffusional creep of a semi-infinitemedium under a cylindrical punch. They found at low punchingstresses, the impressing velocity is proportional to the punchingstress, the lattice diffusivity and inversely proportional to thepunch radius. However, for interfacial diffusion between the punchand the material, it is inversely proportional to the square of thepunch radius. Note that for dislocation creep, the impressing


velocity is dependent on the punching stress and proportional tothe punch radius.

Yang and Li [177] analyzed impression creep of a thin film bylattice diffusion using a straight punch (a 2D problem). They foundthat for a rigid impermeable substrate the impression velocity isdirectly proportional to the film thickness and inversely to thesquare of the punch width. Without the substrate, the impressionvelocity is inversely proportional to the film thickness andindependent of the punch width.

Yang and Li [178] also analyzed impression creep of a thin filmby lattice diffusion using a cylindrical punch. They found, at lowpunching stresses, the impression velocity is proportional to thepunching stress. For the same punching stress and the same punchradius, the impression velocity decreases for a rigid substrate andincreases without the substrate when the film thickness decreases.

Yang and Li [180] analyzed impression and diffusional creepwhen lattice diffusivities are different in all three directions.

Yang and Li [181] analyzed impression creep of a semi-infinitematerial by an annular punch, which is controlled by latticediffusion. They found that, at low punching stresses, the impressionvelocity is proportional to the punching stress. For the samepunching stress, the impression velocity increases without limitwhen the annular thickness approaches zero. For a thin annularpunch, the impression velocity is inversely proportional to thesquare of the thickness for interfacial diffusion and to the thicknessitself for lattice diffusion.

2.7. Dislocation creep

Chu and Li [28] calculated the impression velocity by usingfinite element method in which the strain rate obeys a power lawof the von-Mises stress. They found that the impression velocity isproportional to the punch radius and obeys the same power lawwith the punching stress. To compare with uniaxial creep test, theeffective stress is 0.3 of the punching stress and the effective gagelength is 0.84 of the punch diameter.

Hyde et al. [68] also used finite element method to simulatethe impression creep and found that the equivalent uniaxialstress was 0.296 times the punching stress and the equivalentuniaxial strain rate was the impression velocity divided by 0.755of the punch diameter. These numbers agree with the findingsof Chu and Li [28]. Later Hyde et al. [69] confirmed thesefindings from the impression experiments of 316 stainless steelat 600 8C.

However more recently, Hsueh et al. [62] pointed out that thesenumbers may depend on the stress exponent, n, especially when n

approaches 1. Hyde and Sun [64] and Hyde et al. [65] used arectangular indenter and calculated these numbers by using finiteelement method.

2.8. Stress relaxation

Li [92] reviewed some early work on stress relaxation by using acylindrical indenter. The stress–strain rate relation obtainedagreed with direct dislocation velocity measurements or uniaxialcompression experiments. These relations include power laws andhyperbolic sine stress laws.

2.9. Superplasticity

Shettigar and Rao [147] studied the superplasticity of Pb–Sneutectic alloy of two different grain sizes, 3.4 and 7.5 mm, byimpression testing at temperatures of 30–125 8C. A log–log plot ofstress and strain rate for the fine grain material showed regions (II)and (III) of superplastic behavior. The strain rate sensitivity inregion II was 0.43–0.55 at all temperatures. For the coarse grain




G Model


material the strain rate sensitivity was 0.21–0.45 for which thesuperplasitic behavior was seen only at high temperatures.

Kumar et al. [86] investigated the superplasticity of Zn-22 wt%Al eutectic alloy by the impression creep technique. Forthe small grain size of 0.9 mm in the temperature range of 180–270 8C, a log–log plot between the punching stress and impressionvelocity showed regions I, II and III typical of superplastic behavior.The strain rate sensitivity in region II was in the range of 0.44 to0.51. It was concluded that the impression creep technique is wellsuited for superplasticity studies on small specimen volumes.

2.10. Viscosity measurement

Chen and Li [13] showed that the impression technique can beused to measure viscosity. At low punching stresses, theimpression velocity was proportional to the punching stress, thepunch diameter and inversely proportional to viscosity. Whenthe thickness of the specimen was more than 10 times thepunch diameter, the impression velocity is independent of the stickor slip contact condition at the punch-material interface. Thesefindings were all confirmed by experiments using an ABS polymercontaining 17.5 vol% butadiene. The viscosity varied from 3�1012 Pat 100 8C to 108 P at 150 8C. The activation energy was 208 kJ/molbetween 110 and 156 8C. The viscosity changed abruptly across theglass transition temperature.

Yang and Li [183] found that the relation derived between thepunching stress, punch size, impression velocity and viscosity forsemi-infinite viscous materials was not affected by the non-slip orslip contact condition at the punch/material interface. In fact theydemonstrated this test with amorphous Se. See Ref. [184].

Yang et al. [176] simulated impression creep of Newtonianfluids by using finite element method and found that impressionvelocity became steady if the surface tension/viscosity ratio wasless than 0.1 cm/sec, the product of surface tension and punchradius was less than 0.05 of the applied load and the impressiondepth was less than 1/3 of the punch radius. The steady-statevelocity was proportional to applied load and, for the same appliedload, inversely proportional to viscosity and the punch radius,independent of the non-slip or slip contact condition between thepunch and the material.

Chen and Li [14] analyzed the impression creep of a thin viscouslayer and found that the load required to produce an impressionvelocity is proportional to that velocity, viscosity and the size of thepunch. The proportionality factor was shown to relate to the non-slip or slip boundary conditions between the punch and the viscouslayer and between the viscous layer and the substrate. It was sosensitive to these boundary conditions that the impression testcould be used to detect debonding between the layer and thesubstrate.

Cseh et al. [30] used impression test to measure the viscosity ofglasses at temperatures of 588, 598 and 604 8C. They demonstratedthat impression test can be used to measure the viscosity of glassesin the range of 108–1011 Pa s and calculated the activation energyfor the flow process.

Foerster et al. [39] used impression test to examine the effect ofSi irradiation on the viscosity of polyethylene. The viscosity of theSi-irradiated polyethylene was 10 times of the un-irradiated one,while the irradiation effect was less pronounced for hardness andelastic modulus than for viscosity.

Using a focused ion beam, Rowland et al. [143] produced acylindrical punch of flat end from a silicon sphere and measuredthe viscosity of polystyrene films with contact radius at least fourtimes of the film thickness. They observed a shear-thinningbehavior during the impression of the films and found that theeffective viscosity at a given temperature is lower than thatpredicted by bulk WLF zero shear theory, with the measured


viscosity curve shifted horizontally by 5 8C from the theoreticalcurve. The reason for such a difference is unclear.

2.11. Viscoelasticity

Cheng et al. [20] analyzed the impression behavior of a three-element viscoelastic material by a cylindrical punch. Using therelationships obtained and a flat-ended conical indenter with a 908included angle, they studied the viscoelastic behavior of glassypolystyrene and glassy polyurethane. The measured modulus andviscosity were comparable to the results for bulk polymers. Theissue in the measurement is that the contact area changed with theindentation depth, which makes it dubious to use the relationshipsobtained from the indentation by a cylindrical punch.

Krupicka et al. [85] used impression test to examine theviscoelastic behavior of two thermally crosslinked polymercoatings. One material was a two-layer ductile solvent bornecoating with the top layer being a hydroxy-functionalizedpolyester crosslinked with a blocked isocyanate and filled with5.6 vol% carbon black. The primer was a hydroxy-functionalizedpolyester cross linked with melamine (HMMM) filled with 13 vol%TiO2. The other material was a single-layer flexible powder coatingof carboxy-functionalized polyester crosslinked with triglycidylisocyanurate (TGIC) filled with 36 vol% TiO2. The instantaneousmodulus was independent of indentation depth and a greaterindentation increased the contribution of relaxation modulus.There was good agreement between the relaxation observed intension tests and that at an indentation depth of 25 mm, while pooragreement was observed for the indentation depths of 7–10 mm.

Choi et al. [25] used nanoindentation with a flat ended tip tomeasure the viscoelastic property of PDMS films. Assuming thatthe Poisson ratio of the PDMS films was independent of time, theinitial modulus and relaxation modulus of the PDMS films wereestimated to be 377.51 and 188.58 kPa, respectively. The residualdepth was found to be 10% of the maximum indentation depthabout 15 h after unloading.

Choi et al. [26] used a flat diamond tip to examine theindentation behavior of polymer films (SU-8 and NR4-8000P). ThePoisson ratio and shear modulus of the SU-8 films were 0.22 and1.541 GPa, respectively, which were comparable to the knownvalues. The Poisson ratio and shear modulus of the NR4-8000Pwere 0.40 and 1.461 GPa, respectively. They also evaluated therelaxation modulus which was a function of time.

2.12. Impression adhesion

Yang and Li [187] studied the self-adhesion of PDMS [poly(dimethylsiloxane)] using stainless steel cylindrical punches of0.79, 1.19, 1.59, 2.38, and 3.18 mm radii. A thin film of PDMS ofabout 10 mm thick was coated at the end of the punches. Theyobserved that the pull-off force was proportional to the 3/2 powerof the punch radius and calculated the interface energy at theinstant of separation, which is in accord with Eq. (31). The interfaceenergy increased with the square root of contact time indicating adiffusional process involved in self-healing or bond formation.

Choi et al. [27] measured the time-dependent adhesionbetween SU-8 polymer films (an epoxy-based near-UV photore-sist) and a flat diamond indenter tip. The pull-off force slightlyincreased with the contact time between the film and the indenterand increased with increasing the unloading speed. The adhesionstrength increased from 0.01 to 1 J/m2 when the unloading rateincreased from 100 to 700 nm/s. Their results demonstrated therate dependence of the adhesion strength of polymers.

Guvendiren et al. [60] used impression test to investigate theadhesive behavior of DOPA-modified methacrylic triblock hydro-gels on TiO2 surface in aqueous solution. The adhesion strength




G Model


was dependent on pH value. At pH values of 6 and 7.4, the adhesionstrength was 2 J/m2, which was comparable to the cohesivefracture strength of the hydrogel. At a pH of 10, the hydrogel wasless adhesive and the DOPA groups were hydrophilic.

2.13. Impression Fatigue

Li and Chu [94] performed impression fatigue of a b-tin single-crystal sample with a flat, cylindrical punch and observed thatimpression depth continuously increased with the number ofcycles. They suggested that the continuous penetration of thepunch under a cyclic loading is related to emission of dislocationsdue to stress concentration at the contact edge between the punchand the material.

Xu and Yue [163] performed impression fatigue testing ofpolycrystalline copper with applied stress around 500 MPa andobserved that the penetration depth of the punch per cycle decreasedwith the number of cycles. They suggested that there existed steady-state impression fatigue with the steady-state impression depth percycle increasing with the increase of maximum applied load.

Xu and Yue [164] used a kinematic hardening model to simulateimpression fatigue and compared the simulation results with theimpression fatigue of copper. The simulation results were in accordwith experimental results. The effect of residual stress on thesteady-state penetration depth per cycles was discussed with thepenetration rate decreasing with tensile residual stress andincreasing with compressive residual stress.

Xu et al. [161] studied the effect of overloading on impressionfatigue of polycrystalline copper at room temperature. Theoverloading retarded the penetration depth per cycle and surfacedamage was observed.

Xu et al. [168] did impression fatigue on PVC bulk material andTiN and NiP films/coatings deposited on SUS304 steel substrateand found a simple power law relation between the load amplitudeand the cycles to failure. The failure was detected by in-situacoustic emission during the impression test.

Yang et al. [190] used impression fatigue to examine thedynamic deformation of aluminum. Under the load-controlledcyclic indentation, the punch continuously penetrated into thematerial and reached a quasi-steady state at which the penetrationdepth per cycle was constant. In contrast to the results for theimpression fatigue of copper [163] the steady state penetrationrate decreased with increasing the amplitude of the cyclicindentation load due to the increase in the size of plastic zone.It also decreased with the increase in the mean indentation loaddue to local strain hardening, while it increased with the increaseof the indentation frequency. The reason for the difference isunclear, which might be due to different stress levels.

Yang and Saran [191] used finite element method to simulatecyclic indentation of an elastic–perfectly plastic material by a rigid,cylindrical punch of flat end. The simulation results showed thatthe average penetration depth per cycle increased approximatelylinearly with the amplitude of the cyclic load for the same meancontact load. Also, the average penetration depth per cycleincreased with the mean of the contact load for the sameamplitude of the cyclic load.

Zhao et al. [198] performed impression fatigue of Al alloy 2A12at 200 8C. There was a holding period for both the maximum andminimum contact load. However, they did not discuss the effect ofthe holding time on the impression fatigue.

Some earlier impression fatigue studies were reviewed by Li [93].

2.14. Testing of solder ball grid array

Pan et al. [133] designed a miniaturized impression creepmachine for measuring the creep behavior of tiny solder balls


attached to a ball grid array in a microelectronic packaging system.The punch was a WC cylinder of 100 mm diameter, which waspushed into a solder ball of 750 mm diameter. The temperaturecould be controlled in a range of room temperature to 423 K. Avideo imaging system was used to help with precise alignment ofthe punch with the specimen.

2.15. Nondestructive testing

Impression test could be considered nondestructive since itonly makes a shallow impression on the material surface. Sun et al.[158] suggested using impression test as a life assessment tool forpower plant materials at high temperatures.

2.16. Time to reach steady state

Pan and Dutta [131] suggested a way to reduce the time to reachsteady state impressing creep by first loading with a higher stressand then changing to the desired stress. However, it requiresthe understanding of the effect of the plastic strain created by thehigher stress on the propagation of the plastic zone under theaction of a small desired stress.

2.17. A word on indentation creep

The reason to use a cylindrical indenter with a flat end is toavoid the use of pyramidal, conical or spherical indenters in whicha constant load does not imply constant indentation stress andhence usually does not give a steady state. The creep rate measuredis in a transient state which could be close but also could be faraway from the steady state. Goodall and Clyne [59] showed thisvery clearly for 15 different materials with known results fromconventional creep testing. They did not discuss impression creep.For a review on nanoindentation, (see Ref. [58]). More recently,Stone et al. [156] showed by finite element analysis the strain ratesensitivity of hardness generally differs from that of the flow stress.We will show in this review that the steady state obtained byimpression testing is very close to the steady state obtained byconventional creep testing, demonstrated over and over again bymany people for many materials.

3. Materials tested

3.1. Aluminum alloys

Gollapudi et al. [51] did impression creep of nanocrystalline Alobtained by high pressure torsion of compacted ball-milledpowders. The grain size distribution centered around 30 to40 nm. The testing was done in air. The stress exponent rangedfrom 4.5 to 13.3 in the temperature range of 293 to 381 K and stressrange of 150 to 700 MPa. The activation energy was 69 kJ/mol. Butdue to possible grain growth during creep, the steady state may nothave a stable microstructure. See a model developed by Gollapudiet al. [52] for nanocrystalline materials in general and some data onnc–Al in the section on nanocrystalline materials.

Kutty et al. [90] studied impression creep of Al-22 wt%U-2 wt%Zr and Al-46 wt%U-3 wt%Zr alloys. The stress exponentswere 4.7 and 5.7 respectively at 510 8C. The activation area for thesecond alloy was about 18 b2. The reported values of activationenergy for these alloys were 260 and 318 kJ/mol, respectively,much higher than that of self diffusion, 142 kJ/mol in Al. In theimpression test at 510 8C, 4 to 5 h were needed to reach a steadystate.

Rao et al. [141] studied impression creep of Al-6.3 wt%Cu(AA2219) alloy with Sc, Mg and Zr additions. At 523 K, hightemperature stability was found to increase in the following order:



Table 1Stress exponent and activation energy for Al alloys as measured by impression

creep.

Alloy Stress exponent, n Activation energy, Q (kJ/mol)

523 K 623 K 673 K 150 MPa 225 MPa 300 MPa

AA2219 8 8.1 5.3 94.3 90.7 84.5

0.2%Sc 10 8.2 5.8 112.8 96.1 87.4

0.4%Sc 10.6 8.4 6.3 121.2 103.3 96.7

0.8%Sc 11.3 8.8 6.7 125.5 113.8 99.6

0.2%Sc-Mg 10.2 8.3 6.0 119.2 98.2 87.4

0.2%Sc–Zr 10.3 8.5 7.5 120.2 110.2 106.2

0.2%Sc–Mg–Zr 10.6 8.6 8.1 127.5 115.3 109.3


G Model


AA2219 + 0.8 wt%Sc base alloy, base alloy + 0.2 wt%Zr, basealloy + 0.45 wt%Mg, base alloy + 0.45 wt%Mg + 0.2 wt%Zr. Howev-er, at temperatures higher than 623 K, Zr containing alloysexhibited better high temperature stability than the other twocompositions. Stress exponents and activation energies of all thesealloys are shown in Table 1.

Ketabchi et al. [78] studied the creep behavior of hypo-eutecticAl-12 wt%Si-1.3 wt%Cu-1 wt%Mg-1 wt%Ni (LM13) and hyper-eu-tectic Al-17 wt%Si-1.3 wt%Cu-1 wt%Mg-1 wt%Ni (LM28) pistonalloys. Both alloys were aged and overaged at 623 K for 1 h tostabilize the microstructure. In the temperature range of 490–620 K and punching stress range of 125 to 700 MPa, LM28 had alower creep rate than LM13. The difference was explained by theirmicrostructure.

Liu et al. [96] did impression creep of aluminum alloy 2A12 andobtained a stress exponent of 4.9 � 0.4 at 200 8C between 905 and1415 MPa punching stress which can be compared with 5.3 � 0.7obtained from uniaxial tensile tests at 200 8C between 212 and247 MPa tensile stress. The tensile creep did show a third stage.

Kutty et al. [89] studied microstructural changes of Al-22 wt%Uand Al-46 wt%U containing 3 wt% Zr after heat treatment at 620 8Cfor 1 to 45 days and showed that the (U, Zr)Al3 phase was not stablebut slowly changed to U0.9Al4 phase. This change reflected on theimpression creep curves.

3.2. Copper alloys

Xu et al. [167] did impression stress relaxation on polycrystal-line Cu and obtained strain rate sensitivity, activation strainvolume (b times the activation area) and activation energy andcompared favorably with conventional compression test.

Akbari-Fakhrabadi et al. [1] studied Cu and a Cu-0.3 wt%Cr-0.1 wt%Ag alloy. They found that, to obtain the same impressioncreep rate, the alloy required about 3 times the punching stress ascompared to Cu. Such strength was attributed to the Cr rich phasedistributed in the Cu matrix.

Mahmudi et al. [114] studied impression creep of Cu-0.3 wt%Cr-0.1 wt%Ag alloy. The melted alloy at 1673 K was chill casted into asteel mold, homogenized at 1123 K for 2 h, hot rolled from athickness of 25 to 10 mm and then cold rolled to 5 mm before itwas annealed at 873 K for 30 min. This was the as processedmaterial. Some of the cold-rolled materials were solution treated at1223 K for 1 h, aged at 773 K for 2 h and overaged at 873 K for30 min. This was the aging treated material. The latter was morecreep resistant. The stress exponents were in the range of 5.7 to 8and the activation energy was stress dependent and could beextrapolated to190 kJ/mol at zero stress for both materials. Theactivation energy for lattice diffusion in copper is 197 kJ/mol.Stress relaxation tests showed no internal stress in the asprocessed material but some in the aging treated material.

Akbari-Fakhrabadi et al. [2] used impression test to examinethe creep behavior of a Cu–6Ni–2Mn–2Sn–2Al alloy and the effect


of the addition of 0.3 wt% Cr and 0.3 wt% Zr on the creepdeformation in the temperature range 695–795 K. Using the powerlaw relationship between punching stress and impression velocity,they obtained an average stress exponent of about 4 and activationenergies of 194–196.9 kJ/mol. The values of the activation energieswere close to 197 kJ/mol for lattice diffusion of copper. Theysuggested that the rate process was dislocation climb controlled bylattice diffusion. The addition of 0.3 wt% Cr and 0.3 wt% Zrincreased the creep resistance due to the precipitation of Cr-richand Zr-rich particles in the Cu matrix.

3.3. Lead alloys

Balani and Yang [8] studied the impression creep behavior of90Pb–10Sn alloy and found a power law stress dependence ofimpression velocity with a stress exponent of 4.3 � 0.2 in thepunching stress range of 17 to 103 MPa. An activation energy of46.7 � 3.0 kJ/mol was found in the temperature range of 298 to 393 K.A linear relation between impression velocity and punch diameter forthe same punching stress was shown up to one mm punch diameter.

Pan et al. [133] did impression creep of 90Pb–10Sn ball gridarray solder balls. They found steady state within 1–3 h. The powerlaw exponent was about 4 in the temperature range of 323 to 373 Kand the punching stress range of 10–50 MPa. The activation energywas about 60 kJ/mol.

Mahmudi et al. [110] studied impression creep of the cast Pb-1.25 wt%Sb and Pb-4.5 wt%Sb alloys under a punching stress of 40–135 MPa and at temperatures of 300–420 K. The stress exponentwas 3.3 at low stresses and 12.5 at high stresses for the low Sballoy. These values were 4 and 19 for the high Sb alloy. Theactivation energy was 63 kJ/mol for both materials independent ofstress.

Chen and Yang [15] studied the effect of a DC electric currentpassing through the punch on the impression creep behavior of Pb.They found that the stress exponent increased with the currentdensity at low punching stresses but decreased with currentdensity at high punching stresses. There were some recrystalliza-tion events under the punch which caused some sudden changes inimpression velocity. The impression velocity increased with thesquare of electric current density.

3.4. Magnesium alloys

Azeem et al. [7] did impression creep of short fiber reinforcedQE22 Mg alloy in both the longitudinal and transverse directions.The fibers were Maftech (72 wt% dAl2O3, 28 wt% SiO2), Saffil(>95 wt% dAl2O3, <5 wt% SiO2) and Supertech (65 wt% SiO2,31 wt% CaO, 4 wt% MgO). The punching stress was 62.38 MPa andthe temperature was 473 K. The results were comparable to theconventional tensile creep test in the longitudinal direction.

Peng et al. [135] reported impression creep studies of a Mg alloywith the following weight percent additions, 8Zn, 4Al and 0.5Ca.The stress dependence of impression velocity could be describedby a hyperbolic sine function with a constant activation shearstrain volume of 0.7 � 0.5 nm3. The activation energy was 77.54 kJ/mol for all stresses. A single mechanism of grain boundary fluid flowwas proposed for the creep of this alloy. At the same temperature andpunching stress, the creep rate was inversely proportional to the 3rdpower of grain size in agreement with the model.

Kondori and Mahmudi [84] studied impression creep of a Mg-6 wt%Al-0.3 wt%Mn alloy (AM60). The stress exponent was 8 to 12in the high stress region and 4 to 6 in the low stress region. Theactivation energy was 134 to 165 kJ/mol in the high stress regionand 76 to 84 kJ/mol in the low stress region. Two separatemechanisms were suggested to operate in the two regions. Butthey did not try the hyperbolic sine stress dependence.




G Model


Kabirian and Mahmudi [73] studied the impression creepbehavior of a cast Mg-9 wt%Al-1 wt%Zn-0.3 wt%Mn (AZ91) alloy.The microstructure consisted of b-Mg17Al12 intermetallic phase inthe a-Mg matrix. The intermetallic phase is thermally unstable andprone to coarsening during creep. The stress exponent was in therange of 4.2 to 6.0 and the activation energy in the range of 94 to123 kJ/mol for a punching stress of 0.02 to 0.04 G.

Kabirian and Mahmudi [74] studied the effect of rare earthadditions on the creep resistance of Mg-9 wt%Al-0.8 wt%Zn-0.3 wt%Mn (AZ91) alloy. They added 0, 1, 2 and 3 wt% RE, mainlyLa and Ce. In that order, the stress exponents were 4.9 to 6.0, 5.6to 6.8, 5.3 to 6.7 and 6.0 to 7.0 depending on temperature (425 to525 K). The corresponding activation energies were 94 to 113, 90 to118, 96 to 110 and 102 to 126 kJ/mol depending on punching stress(0.024 to 0.036 G) with G being shear modulus. The strengtheningeffect was attributed to the formation of Al11RE3 intermetalliccompounds.

Mondal and Kumar [121] studied the impression creepbehavior of AE42 Mg alloy reinforced with Saffil short fibers andSiC particles in various combinations. Punch was perpendicular tothe fibers. Punching stress ranged from 60 to 140 MPa andtemperature ranged from 175 to 300 8C. The stress exponent was 4to 7 after the internal stress was subtracted. The creep curvesobtained at high stresses and temperatures differed significantlyfrom those obtained at low stresses and temperatures which werenormal. At 300 8C and 120 MPa the strain rate started low,increased to a maximum and decreased.

Nami et al. [123] studied impression creep of AZ91 (see above)and AZRC91 (AZ91 + 1 wt%RE + 1.2 wt%Ca) alloys. The latter wasmuch more creep resistant due to the additional intermetalliccompounds formed. The stress exponents were 5.69 to 6 for AZ91and 5.81 to 6.46 for AZRC91. The corresponding activation energieswere 120.9 � 8.9 and 100.6 � 7.1 kJ/mol.

Kabirian and Mahmudi [72] studied the effect of Zr additions onthe creep resistance of Mg-9 wt%Al-0.8 wt%Zn-0.3 wt%Mn (AZ91)alloy. They added 0, 0.2, 0.6 and 1.0 wt% Zr. The improved creepresistance was attributed to the formation of nanosized Al2Zr andAl3Zr2 intermetallics. The stress exponents and activation energiesfor all the alloys were tabulated.

Nayyeri and Mahmudi [128] studied impression creep of a castMg-5 wt%Sn alloy. Some were aged at 483 K for 20 h. The stressexponents were 5.2 to 5.7 for the cast samples and 6.8 to 6.9 for theaged samples. The corresponding activation energies were 98 and90 kJ/mol. Nayyeri et al. [130] found the strengthening effect of1.4 wt%Ca additions or 0.4 wt%Sb additions to this alloy due to theformation of thermally stable compound of CaMgSn or Mg3Sb2.

Nayyeri and Mahmudi [126] studied the effect of 0.15, 0.4 and0.7 wt% Sb additions on the impression creep behavior of as-castMg-5wt%Sn alloy. The Mg-5 wt%Sn-0.4 wt%Sb had the highestcreep resistance due to the formation of blade-shaped thermallystable precipitates of Mg3Sb2 which strengthened both grains andgrain boundaries and prevented recovery and recrystallizationduring creep at high temperatures. The impression creep experi-ments were carried out within 423–523 K and 150–475 MPa. Thecreep behavior was different in the high and low stress regions. Thelow stress region showed a stress exponent of 5–6 and anactivation energy of 97 kJ/mol while the high stress region showeda stress exponent of 10–12 and an activation energy of 162 kJ/mol.

Nayyeri and Mahmudi [127] studied impression creep of castMg-5 wt%Sn–x wt%Ca alloys with x = 0.7, 1.4 and 2. The alloy withx = 2 had the lowest creep rates due to the formation of thermallystable CaMgSn phase within the matrix and in grain boundaries.The stress exponents were 5 to 6 in the low stress region and 10 to12 in the high stress region with corresponding activation energiesof 97 and 163 kJ/mol. The effect of internal stress should beinvestigated.


Nayyeri and Mahmudi [129] reported that the addition of Ca tothe Mg-5wt%Sn alloy with refined dendritic microstructuresuppressed the formation of Mg2Sn and enhanced the formationof rod shape and lamella precipitates of CaMgSn. These effectsincreased the creep resistance. Prolonged annealing at 300 8Csoftened and dissolved Mg2Sn but left behind CaMgSn whichstrengthened the material due to its thermal stability.

Keyvani et al. [79] studied impression creep of 5 alloys, Mg-5 wt%Sn, and the 4 separate additions, 1 wt% rare earth (Ce richmisch-metal), 3 wt%Bi, 0.4 wt% Sb and 2 wt% Ca. The last one wasthe most creep resistant due to the formation of large volumefraction of CaMgSn particles.

Alizadeh and Mahmudi [3] studied the strengthening effect of Siand Sb additions on the impression creep behavior of Mg-4wt%Znalloy. Under a punching stress of 250 MPa at 200 8C, thepenetration depth reached 0.3 mm for the Mg–4Zn alloy in about13 min but only 0.18 mm in 1 h for the Mg–4Zn–2Si alloy and only1 mm in 1 h for the Mg–4Zn–2Si–0.2Sb alloy. The strengtheningeffect was attributed to the thermally stable Mg2Si and Mg3Sb2

precipitates.Golmakaniyoon and Mahmudi [53] doped Mg-6 wt% Zn-

2.7 wt% Cu-0.4 wt% Mn (ZC63) alloy with 0, 1, 2 and 3 wt% of arare earth alloy (71.5 wt% La, 10.2 wt% Ce, 6.5 wt% Nd and 11.8 wt%Pr). The increased creep resistance was attributed to the thermallystable phases formed between Mg (and Cu) with the rare-earthelements. The stress dependence of impression velocity showedtwo regions, a low stress region with a stress exponent of 4.4–6.0and a high stress region with a stress exponent of 7–12.7. Theactivation energies were also different, 73–78 kJ/mol in the lowstress region and 122–130 kJ/mol in the high stress region. Laterthey compared the effects of La- and Ce-rich rare earth additionsand found that Ce-rich rare earth additions were more effective.See Ref. [54].

Nami et al. [124] studied impression creep of semi-solidprocessed Mg alloy with the following wt% of elements 9.2Al,0.91Zn, 0.21Mn, 1.18Ca and 0.95La (AZRC91). The improved creepresistance by Ca and La additions was attributed to the formationof Al2Ca and Al11La3 intermetallic compounds. The stress exponentranged from 4.9 to 7 in the temperature range of 425 to 485 K andthe activation energy ranged from 87 to 108 kJ/mol in the stressrange of 0.025 to 0.035 G with G being the shear modulus.

Keyvani et al. [80] studied impression creep of Mg-5 wt%Sn–x wt%Bi alloys with x = 0, 1, 2 and 3. Without Bi the microstructureconsisted of a-Mg dendrites and lamellar eutectic of a-Mg andMg2Sn at grain boundaries. Addition of Bi changed the Mg2Snparticles to spherical shape and some rod shaped Mg3Bi2

intermetallic compounds were formed. Increasing Bi contentconverted more Mg2Sn particles into Mg3Bi2 and increased thecreep resistance. Without Bi the stress exponents were 5 to 5.7 inthe low stress region and 10 to 11.4 in the high stress region. Theactivation energies were 98 kJ/mol in the low stress region and164 kJ/mol in the high stress region. Addition of Bi showed a singlestress exponent of 7 to 8 and an activation energy of 107, 105.6 and101 kJ/mol for x = 1, 2 and 3, respectively.

Kashefi and Mahmudi [76] studied the effect of 0.5, 1.0 and2.0 wt% yttrium additions on the impression creep of as-cast AZ80Mg alloy in the temperature range of 423 to 523 K. The punchdiameter was 2.0 mm, and the sample thickness was 2.5 mm. Theyobserved that, at low temperatures up to 473 K, the AZ80 + 0.5Yalloy had the largest creep resistance, and the AZ80 + 1.0Y alloyhad a better performance for the temperature in the range of 473 to523 K. They suggested that the presences of b-Mg17Al12 and Al2Yphases together with solid solution hardening effect of Al in the Mgmatrix strengthened the AZ80 + 0.5Y alloy at low temperatures. Athigher temperatures, a higher volume fraction of the morethermally stable Al2Y and lower amounts of the less stable




G Model


b-Mg17Al12 improved the creep behavior of AZ80 + 1.0Y. The stressexponents and activation energies were 6.0–8.8 and 90–119 kJ/mol, respectively. There was particle strengthening effect at highstresses. Addition of 2.0 wt% yttrium to AZ80 alloy reduced thecreep resistance due to less solid solution hardening.

Alizadeh et al. [5] performed the impression creep tests of theas-cast and aged Mg-4 wt% Zn alloy in the temperature range of423–523 K. The ageing treatment improved the creep resistance ofthe alloy. The stress exponent values of both the as-cast and theaged alloys were close to each other and were in the range of 4–6and 8–10 in the low and high-stress regimes, respectively. Theactivation energy values were stress-dependent. For the as-castalloy, the average activation energies were 92 � 5 and 45 � 5 kJ/mol for 0.0039 < s/G < 0.0047 and 0.0029 < s/G < 0.0041, respec-tively. For the aged alloy, the average activation energies were82 � 5 and 69 � 5 kJ/mol for 0.0096 < s/G < 0.0117 and0.0071 < s/G < 0.0091, respectively. They suggested that stress-assisted dislocation climb was the rate-mechanism for the creep ofthe as-cast and aged alloys.

Mahmudi and Moeendarbari [115] used impression test tostudy the creep behavior of an AZ91 Mg alloy with the addition of0.5, 1.0, and 2 wt% Sn in the temperature range of 423–523 K. Thepunch diameter was 2 mm, and the sample thickness was 3 mm.The alloy with 2 wt% Sn had the largest creep resistance due to theformation of Mg2Sn which reduced the fraction of eutectic b-Mg17Al12 phase and the effect of solid solution hardening from Aland Sn. They obtained the stress exponent of 5.0–6.9 and theactivation energy of 110–150 kJ/mol. Using the sectioningtechnique, they found that there existed three regions under theindentation: (1) dead zone directly under the contact interfacebetween the punch and the sample, in which there was no visibledeformation, (2) flow zone directly under the dead zone, in whichmaterial flow occurred, and (3) deformation-free zone far awayfrom the contact interface. They suggested that there existed twoparallel rate-processes; one was the lattice diffusion-controlleddislocation climb and the other was the pipe lattice diffusion-controlled dislocation climb.

Ansary et al. [6] compared the results of the impression creep ofAZ31 Mg alloy with those of tensile creep in the temperature rangeof 423–498 K. They found that the creep behavior could be dividedinto two stress regimes with different stress exponents andactivation energies. From the impression tests, the stress exponentand activation energy were 3 and 96.9 kJ/mol for low stresses,respectively, and the stress exponent and activation energy were 6and 126.6 kJ/mol for high stresses, respectively. Both the stressexponents and the activation energies obtained from the impres-sion tests were comparable to those obtained from the tensiletests. They did not try to use the hyperbolic sine relationshipbetween punching stress and impression velocity to analyze thecreep results.

Geranmayeh and Mahmudi [45] performed the compressionand impression creep of a cast Mg–Al–Zn–Si alloy in thetemperature range of 423–523 K. They observed that the creepdeformation can be divided into two stress regimes. The stressexponents were 4–5 and 10–12 for low stresses and high stresses,respectively. The corresponding activation energies were 90 and141 kJ/mol, respectively. The impression results were comparableto the compression results. They did not use the hyperbolic sinerelationship between stress and creep rate to analyze the creepresults.

Geranmayeh et al. [46] used impression test to study the creepbehavior of AZ61 and AZ61–0.7Si Mg alloys in the temperaturerange of 298–523 K. They observed that the addition of Sisignificantly increased the creep resistance of AZ 61 due to theformation of Mg2Si intermetallic particles and the reduction ofb-Mg17Al12 phase.


3.5. MoSi2

Butt et al. [11] studied impression creep of SiC–MoSi2

composites with 0 to 40%SiC by volume at 1000 to 1200 8C under258–362 MPa punching stress. Finite element analysis was used tocompare impression creep with compression creep data ofSadananda et al. [144,145]. They showed similar relations betweensteady state creep rate and the volume fraction of SiC, and betweenthe stress exponent and the volume fraction of SiC. The activationenergy obtained from impression creep seemed to increase withthe volume fraction of SiC but that from compression creep[144,145] seemed to decrease with the volume fraction of SiCalthough the values were in the same range of 400–700 kJ/mol.

Petrovic et al. [136] evaluated the effect of MoSi2 on theimpression creep of Si3N4 composites at 1200 8C and 310 MPa.They found that fine-phase composites were more creep resistantthan coarse-phase composites. The steady-state creep rateincreased with increasing the volume fraction of MoSi2.

Doreakova et al. [34] did impression creep of monolithic MoSi2

within 1100 and 1250 8C and under a punching stress of 20 to100 MPa. The stress exponent was about 1 and the activationenergy was about 250 kJ/mol. The results were compared withthose from the bending test.

3.6. Nanocrystalline materials

Gollapudi et al. [52] developed a model for impression creep ofnanocrystalline materials. In this model, a stress-assisted graingrowth including grain coalescence and grain boundary migrationwas proposed during creep. Creep deformation will cease when thestress is not sufficient to support grain growth. No steady statecreep was possible so the parameters obtained were not the sameas steady state creep. Data on nc–Al and nc–Zn-22 wt%Al wereshown.

3.7. Ni alloys

Wang et al. [159] studied impression creep of HP40Nb alloy, aNi–Cr high temperature alloy being used in petrochemical plants.Specimens were cut from serviced components and heat treated atdifferent temperatures from 900 to 1250 8C to simulate workingconditions. Impression creep tests were done at 900 8C and under apunching stress of 150 MPa. They showed transient and steadystate stages. The effect of heating temperature was shown.

Xu et al. [166] did computer simulation of impression creep onthe three faces [0 0 1], [ 01 1] and [1 1 1] of a single crystal Ni. Thesurface patterns developed showed 4-, 2- and 3-fold symmetry,respectively. The stresses remained after unloading were shown.

3.8. Polymers

Chiang and Li [22] did impression creep of ABS polymers(acrylonitrile–butadiene–styrene) with different butadiene con-tents under punching stresses of 10–120 MPa in the temperaturerange of 330–390 K (glass transition 376 K). The creep resistancedecreased but the activation strain volume increased withincreasing amount of butadiene. The activation strain volumewas not affected by stress or temperature. The activation energystarted at 100 kJ/mol at 340 K increased to 200 at 360 K, 400 at370 K, 800 at 375 K and reached a maximum of 1100 kJ/mol at380 K and then decreased to 500 kJ/mol at 390 K.

Chiang et al. [23] did compression creep test of ABS polymers tocompare with the impression creep test. The temperature andstress dependences of the steady creep rate were generally inagreement with such dependences of the impression velocitybelow 353 K but started to deviate at high temperatures.



Table 2Stress exponent and activation energy for the creep of SiAlOG ceramics.

Methodology Composition Activation

energy (kJ/mol)

Stress exponent

Impression A 523 � 73 2.06 � 0.31

B 446 � 93 2.40 � 0.72

C 717 � 57 1.48 � 0.62

Compression A 504 � 52 0.87 � 0.17

B 539 � 40 0.88 � 0.14

C 418 � 67 0.95 � 0.60


G Model


Chen and Li [13] used impression test to measure the viscosityof ABS polymers containing 17.5 vol% butadiene (see Section 2.10for more details).

Chang and Yang [12] did impression test on a polypropylenecopolymer to avoid necking in a tension test and yielding in acompression test. The impression test showed only work harden-ing. The punching stress-punching strain (depth divided by punchdiameter) curves were independent of the punch diameter of 0.5, 1and 2 mm. The 0.2% offset yield stress and the UTS obtained fromthe impression test agreed with those from the uniaxial tests. Theelastic modulus, strain hardening exponent and strain ratesensitivity were also determined from the impression test.

Yang [171] used impression creep to measure the viscosity ofpolycarbonate in a temperature range of 419 to 443 K and underpunching stresses between 0.25 and 20 MPa. He found that theflow behavior of polycarbonate under these conditions isNewtonian and the activation enthalpy is 413 kJ/mol.

Yang and Li [185] did impression creep test on PMMA to a depthof 0.3 mm and watched the disappearance of the impression at thesame temperature when the load was removed. The rate ofdimensional recovery obeyed second order kinetics and thetemperature dependence of the rate constant showed twoconsecutive processes with activation energies 440 kJ/mol be-tween 104 and 113 8C and 95 kJ/mol between 113 and 140 8C. Twopairs of defects of opposite signs are believed to be involved in thedimensional recovery.

Shinozaki et al. [151] studied kink bands developed duringimpression testing of oriented polypropylene (see Ref. [97]).Molten material was held at 190 8C for 30 min before slow cooling.Tensile bars were cut and hot drawn at 123 8C at a strain rate of0.19 s�1 to a draw ratio of 8. The hardened steel punch had 80 mmdiameter with a polished flat face. Punching was done at 0.22 mm/sfor a maximum depth of 80 mm. For dynamic testing the amplitudewas 36 mm at 2 Hz. The kink band exhibited negative dampingproperties probably due to negative work hardening from localizedbuckling of oriented polypropylene.

Li et al. [95] did the contact measurement of internal fluid flowwithin poly(n-isopropylacrylamide) gels by using a flat cylindricalpunch and a flat rectangular punch under oscillatory loadingconditions. The frequency was in the range of 0.01 to 10 Hz. Theshear modulus at 22 8C was independent of the frequency, while itincreased with the frequency at 39 8C. The phase angle decreasedwith the frequency in the frequency range of 0.01 and 0.1 Hz andindependent of the frequency in the range of 0.1 to 1 Hz at 39 8C.

Chen et al. [19] did impression creep of PMR-15 at 563 to 613 Kand under a punching stress of 76 to 381 MPa. The stress exponentwas 1.5–2.2 and the activation energy was 122.7 � 6.1 kJ/moldecreasing slightly with increasing punching stress. For the samepunching stress, the impression velocity was proportional to thepunch diameter.

3.9. Power plant materials

Sun et al. [158] proposed to use the impression creep techniqueto predict the service life of components. They think impressiontest is a potential, simple and economic life assessment tool.

3.10. SiAlON ceramics

Fox et al. [40] did both impression and compression creep ofYb–SiAlON ceramics. Three compositions, A, B and C were used. Aand B were a mix of equiaxed a-SiAlON grains and elongated b-SiAlON grains with a glassy intergranular phase. For C, both phaseswere equiaxed and virtually no intergranular glass. A, B and Ccontained 28, 32 and 57 wt% a and had b-SiAlON values of 0.5, 0.9and 1.0, respectively. Temperature ranged from 1300 to 1400 8C.


Compressive stresses were 100 to 300 MPa. Punching stresseswere 200 to 400 MPa. Some of the results are listed in Table 2.

3.11. Stainless steel

Naveena et al. [125] used impression test to study the effectof nitrogen on the creep deformation of 316LN stainless steel at923 K. The fraction of nitrogen was 0.07, 0.11, 0.14, and0.22 wt%, and the creep tests lasted up to 1000 h. They observedthat the steady state impression velocity decreased withincreasing the fraction of nitrogen, and the stress exponentsvaried between 3.3 and 8.2 which decreased with increasing thefraction of nitrogen.

Mathew et al. [117] performed the impression creep tests of316LN SS containing 0.07, 0.14, and 0.22 wt% nitrogen at 923 K.They observed that the equivalent steady-state creep ratescalculated from impression velocities were in good accord withthe steady-state creep rates obtained from conventional uniaxialcreep tests. The impression velocity decreased with increasingnitrogen content.

3.12. Thermal barrier coatings

Yan et al. [170] made an attempt to separate the contributionsfrom thermal barrier coatings and from bulk substrate by usingimpression test as it varied with the punch size since the smallerthe punch the more contribution would be from the coating.

3.13. Thin films

Yang and Li [177,178] analyzed the diffusional creep in a thinfilm by impression testing with a straight punch and also with acylindrical punch.

Xu et al. [162] did finite element analysis of a punch-thin film-substrate system. They found that the friction between the punchand the thin film was not important. The maximum von Misesstress and the maximum shear stress at the film/substrateinterface increased with the substrate/film modulus ratio. Theyalso increased with the thickness of the film. The steady stateimpression velocity increased with the film/substrate modulusratio and also with the thickness of the film. They did notconsider the contribution of substrate creep to the impressioncreep.

Xu and Yue [165] did finite element analysis of punching athree-layer system and found a way of measuring the yield stressesand strain hardening of the top and middle layers by using punchesof two different sizes. It is worth mentioning that the plasticdeformation of substrate can be important for the impression ofultrathin films and small ratio of the film thickness to the punchradius.

Cross et al. [32] did impression test of 36 nm polymer films witha 185 nm diameter punch at 20 to 125 8C with indenting rates of 1–100 nm/s. Instrumented imprint is a new material testing platformenabling measurements of soft matter properties in thin film-confined geometries.



Table 3Stress exponent for the creep of tin alloys.

Indentation creep Impression creep

Pure tin 8.9 7.8

Sn-37 wt%Pb 6.1 5.3

Sn-1 wt%Zn 8.0 7.8

Sn-0.7 wt%Cu 9.7 9.1

Sn-0.7 wt%Cu-1 wt%Zn 9.5 8.6


G Model


3.14. Tin-based solders

Chu and Li [29] studied the impression creep behavior of singlecrystals of Sn in the [0 0 1], [1 0 0] and [1 1 0] orientations. Thetemperature dependence of impression velocity showed twoparallel processes. The high temperature process had an activationenergy of about 107 kJ/mol for all three orientations independentof stress. This value is similar to that for self diffusion in Sn. For thelow temperature process the activation energy was stress-dependent. Some values were 34 kJ/mol for the [0 0 1] orientationat 16–20 MPa, 42 kJ/mol for [1 0 0] orientation at 12–16 MPa and39 kJ/mol for the [1 1 0] orientation at 16–20 MPa. For allorientations and all temperatures, the stress exponent wasbetween 3.6 and 5.0.

Park et al. [134] studied impression creep of polycrystalline Sn.They found the stress exponent was about 5 and the activationenergy was about 42 kJ/mol. These values were comparable tothose obtained by compression creep.

Shettigar and Rao [147] studied superplasticity of Pb–Sneutectic alloy of two different grain sizes, 3.4 and 7.5 mm. SeeSection 2.9 for some details.

Yang and Li [179] studied impression creep of 63Sn–37Pbeutectic alloy and found a hyperbolic sine stress dependence ofimpressing velocity with a single activation energy of 55 kJ/mol.Long and steady impression velocity was observed at each stresslevel. The creep data obtained from stress relaxation agreed wellwith impression creep. For the same punching stress, theimpression velocity is proportional to the punch diameter andinversely proportional to the nth power (n = 1–3) of eutecticparticle size. The mechanism proposed was interfacial viscousflow.

Rani and Murphy [137] studied impression creep of Sn-58%Bi,Sn-57Bi-1.3Zn and Sn-38Pb alloys at 303–393 K under 2.6–180 MPa punching stress. Stress exponent was 2 to 6.3 andactivation energy was (extrapolated to zero stress) 155, 120 and112 kJ/mol for the three alloys, respectively and all stressdependent. For example, at 60 MPa, these numbers were 115,90 and 70 kJ/mol, respectively within the measured range.However, the effect of punch size on impression velocity wasnot quite right.

Pan et al. [133] designed a miniaturized impression testmachine for ball grid array solder balls and tested a 90Pb–10Snalloy.

Pan et al. [132] also studied the impression creep behavior of90Pb–10Sn alloy. Below the solvus temperature (408 K) the Sn richbeta phase was dispersed in equiaxed grains of Pb rich alpha withless than 5 wt% Sn. The stress exponent was about 4 and theactivation energy was 60 kJ/mol. Above the solvus, the entire10 wt% Sn was in solution and the stress exponent was about 3 andthe activation energy was 92 kJ/mol.

Dutta et al. [37] studied the impression creep of rapidly cooledSn–3.5Ag solders. They found a transition from low to high stresssensitivity with increasing punching stress. Following slight agingthe solute concentration dropped to near-equilibrium valueswhich affected the low stress mechanism.

Table 4Stress exponent and activation energy for the creep of hypoeutectic Sn–Zn alloys.

Material Particle volume fraction Activation energy (kJ

Sn-2.5 wt%Zn 1.8 41.9

Sn-4.5 wt%Zn 3.1 43.9

Sn-6.5 wt%Zn 6.3 44.5

Sn-9 wt%Zn 8.3 46.0


Yang and Peng [189] studied the impression creep of Sn–3.5Agalloy in the temperature range of 333 to 453 K under a punchingstress of 3.4 to 67 MPa. The steady state impression velocity variedwith a hyperbolic sine function of stress with an activation energyof 51 kJ/mol independent of stress. They suggested a grainboundary fluid flow mechanism.

Srinath and Aswath [155] studied the impression creep of Sn–3.5Ag and Sn–3.5Ag–0.5Cu alloys and found higher creepresistance as compared to the eutectic Sn–Pb solder under allthe testing conditions. Composite solders (Sn–3.5Ag + 5 wt%Cu orAg, Sn–3.5Ag–0.5Cu + 5 wt%Cu or Ag) performed better thanmonolithic solders and Cu reinforcement was better than Agreinforcement.

Chen and Yang [17] studied the effect of a DC electric currentpassing through the punch on the impression creep of a Sn60Pb40alloy. They found that the steady state impression velocityincreased with electric current at the same punching stress andthe stress dependence of the impression velocity followed ahyperbolic sine law of punching stress. The activation energydecreased linearly with the square of electric current. They alsostudied the contact heating problem due to the passing of electriccurrent. See Ref. [18].

Chen and Yang [16] studied the effect of a DC current passingthrough the punch on the impression creep behavior of Sn. Thesteady state impression velocity obeyed a hyperbolic sine law ofpunching stress. The activation strain volume increased linearlywith temperature. The activation energy decreased linearly withthe square of electric current.

Rezaee-Bazzaz and Mahmudi [142] studied the impressioncreep of Sn-40 wt% Pb-2.5 wt% Sb peritectic alloy. They found thatthe stress exponent increased with stress for the alloy of 2.4 mmgrain size but stayed constant at 2.8 for the alloy of 5.0 mm grainsize. The activation energy was stress-independent and averaged52.0 kJ/mol for the smaller grain size and 54.5 kJ/mol for the largergrain size.

Mahmudi et al. [116] evaluated the stress exponents of Sn-40 wt%Pb-2.5 wt%Sb solder alloy by impression creep testing,impression stress relaxation, indentation creep testing andtraditional creep testing at room temperature. In that order, thestress exponents were 2.55, 2.63, 2.58 and 2.60 for the finer grainmaterials (grain size 2.4 mm) and 2.80, 3.12, 2.71 and 3.20 for thecoarser grain materials (grain size 5.0 mm).

Mahmudi et al. [109] studied the impression creep of Sn-5 wt%Sb alloy. For the cast material with a coarse grain structureand low volume fraction of particles, a stress exponent of 5.4 andan activation energy of 53.8 kJ/mol were obtained in the low stress

/mol) Stress exponent n

298 K 320 K 340 K 370 K

6.6 6.1 6.0 6.0

6.6 6.5 6.3 6.1

7.4 7.3 7.3 7.1

7.5 7.3 7.3 7.2




G Model


region. In the high stress region, a stress exponent of 11.4 and anactivation energy of 75.8 kJ/mol were obtained. For the wroughtmaterial, a stress exponent of 2.8 and an activation energy of41.3 kJ/mol were obtained over the whole stress (20 to 60 MPa)and temperature ranges (298 to 403 K) studied.

Mahmudi et al. [106] studied the impression creep of somedilute tin alloys. The stress exponents obtained at room tempera-ture are given in Table 3.

Mahmudi et al. [107] studied the impression creep ofhypoeutectic Sn–Zn alloys. The results are tabulated in Table 4.

Mahmudi et al. [108] studied the impression creep of Sn-9 wt%Zn, Sn-9 wt%Zn-0.5 wt%Ag, and Sn-9 wt%Zn-0.5 wt%Alalloys. The last alloy had the highest creep resistance. The stressexponents and activation energies were, respectively, 6.9, 7.1 and7.2 and 42.1, 42.9 and 43.0 kJ/mol. The range of punching stresswas 60 to 130 MPa and the range of temperature was 298 to 370 K.

Mahmudi et al. [112] studied the impression and indentationcreep of Sn-3.8 wt%Ag and Sn-–3.8 wt%Ag-0.7 wt%Cu alloystogether with Sn-37 wt%Pb for comparison. The stress exponentswere 5.1 for the Sn–Pb alloy, 9.4 for the Sn–Ag alloy and 9.6 for theternary alloy. The corresponding numbers from indentation testswere 5.5, 9.6 and 9.7.

Mahmudi et al. [105] studied impression creep of Sn-9 wt%Znand Sn-8 wt%Zn-3 wt%Bi alloys at room temperature. The ternaryalloy was more creep resistant than the binary alloy. For the binaryalloy, the stress exponents were 8.5 from impression creep, 8.6from indentation creep and 8.7 from impression stress relaxation.For the ternary alloy, the corresponding values were 9.8, 10.2 and9.7, respectively.

Mahmudi et al. [113] studied the impression creep of Sn-9 wt%Znwith 0.1, 0.25 and 0.5 wt% rare earth (mostly La and Ce) additions.The one with 0.25 wt% RE showed the highest creep resistance due tothe formation of Sn–RE intermetallics. More rare earth mightremove Zn from the matrix and reduce the volume fraction of Zn richparticles. The stress exponent was about 7 and the activation energy46 kJ/mol.

Mahmudi et al. [111] studied the impression creep of Sn-2 wt%Bialloy with 0.1, 0.25 and 0.5 wt% rare earth (manly Ce and La)additions. The one with 0.25 wt% RE had the lowest creep rate. Thereason is similar to the above story. The stress exponent was in therange of 8–10.5, 8.4–11.5, 8.8–12.3 and 8.4–116 for the alloy itselfand 0.1, 0.25 and 0.5 wt% RE additions, respectively. The corre-sponding activation energies were 64.5, 65.1, 67.4 and 68.0 kJ/mol inthe stress range of 70 to 190 MPa and a temperature range of 298 to370 K.

Kangooie et al. [75] studied the impression creep of a Sn-1.7 wt%Sb-1.5 wt%Ag solder alloy with and without 2.3 wt%submicron alumina particles. The addition of alumina particlesincreased the creep resistance. But both the stress exponents of 5.3to 5.9 and the activation energies of 42 to 44 kJ/mol were similarfor both alloys.

Mahmudi and Geranmayeh [102] studied the impression creepof several dilute Sn alloys at room temperature. The stressexponents observed are shown in Table 5.

Table 5Stress exponent for the impression creep of dilute Sn alloys at room temperature.

Material Melting

temp (K)

Impression Indentation

dh/dt vs. Hv

Indentation

Hv vs. time

Pure Sn 505 7.8 7.9 8.4

Sn-0.7 wt%Cu 500 9.1 9.0 9.6

Sn-3.8 wt%Ag 498 9.4 9.3 9.9

Sn-9 wt%Zn 471 9.0 9.3 9.8

Sn-5 wt%Sb 518 4.4 and 11.4 11.5 12.0

Sn-2 wt%Bi 502 3.5 and 12.8 14.3 14.7


Mahmudi et al. [100] observed superplasticity of Sn-5 wt%Sballoy with a grain size of 2.5 mm. The impression rate-punchingstress dependence showed three distinct regions with the middleregion having a stress exponent of 1.7–2.4 in the temperaturerange 298–340 K and an activation energy of 42 kJ/mol. However,the grain coarsened at 370 K and the stress exponent increased to3.4.

Mahmudi and Eslami [101] studied the impression creepbehavior of Zn-20 wt%Sn, 30 wt%Sn and 40 wt%Sn solders. Theyfound that the steady state impression velocity had a power lawdependence of punching stress with a stress exponent of 4.0 to 6.1in the range of punching stress of 50 to 200 MPa. The activationenergy was in the range of 40 to 45 kJ/mol in the temperaturerange of 298 to 425 K. Increasing Sn content reduced the creepresistance of the Zn alloy.

Mahmudi et al. [103] studied the effect of cooling rate on theimpression creep of Sn-9 wt%Zn and Sn-8 wt%Zn-3 wt%/Bi soldersat room temperature. Two cooling rates, 0.01 and 8 C/s were used.The faster cooling rate for the binary alloy showed much morecreep resistant due to the uniform distribution of fine Zn particles.Addition of Bi increased the creep resistance in both conditions dueto solid solution hardening but the effect of cooling rate was notthat pronounced. The stress exponent of 6.2 (slow cooling) and 8.5(fast cooling) for the binary alloys and 9.3 (slow cooling) and 9.8(fast cooling) for ternary alloys agreed with those from conven-tional creep tests at room temperature.

Later these same authors [105] compared the stress exponentsat room temperature for the binary and ternary alloys by usingimpression creep (8.5 and 9.8), indentation creep (8.6 and 10.2)and impression stress relaxation (8.7 and 9.7) tests and found thatthey were similar as shown. The ternary alloys had higherexponents due to both solid solution and precipitation hardening.More recently they [104] studied the effect of isothermal aging onthe impression creep behavior of the same two alloys at roomtemperature. Aging for 10 h at 370 K reduced the creep resistanceof the binary alloys but increased the creep resistance of theternary alloys.

Geranmayeh et al. [47] studied the impression creep of lead-free Sn–5Sb solder alloy containing Bi and Ag in the temperaturerange of 298–373 K. The Sn–5Sb–1.5Bi had the largest creepresistance due to the solid solution hardening of Bi in Sn. Theformation of Ag3Sn intermetallic compound improved the creepresistance of the Ag-containing alloys. The average stressexponents of 5.3, 6.0, 5.6 and 5.1 were obtained at low stressesand 11.5, 12, 11.7 and 10.5 at high stresses for Sn–5Sb, Sn–5Sb–1.5Bi, Sn–5Sb–1.5Ag and Sn–5Sb–1Ag–1Bi, respectively.

The activation energy was in the range of 40.6–53.8 kJ/mol forlow stresses, and the activation energy was 72 kJ/mol for highstresses.

3.15. Titanium aluminide

Dorner et al. [36] did impression creep on a TiAl alloy (Ti-47Al-2Mn–2Nb + 0.8 vol%TiB2 XDTM produced by Howmet Corp (White-hall, USA)). Cast rods were HIPed (1260 8C, 172 MPa) followed by aheat treatment in vacuum at 1010 8C for 50 h. The alloy had aduplex microstructure with 15–20 vol% lamellar a2 + g grains(30 mm) and equiaxed g grains (15 mm). No preferred orientationwas developed. The cylindrical alumina punch had 1 mm heightand 1 or 2 mm diameter. The sample cylinder had 8 mm height and15.5 mm diameter. A stress exponent of 3.2 was obtained at1050 8C and 50–100 MPa punching stress. It was 5.2 at 900 8C and200–650 MPa and 7.6 at 750 8C and 810–1430 MPa. The exponent7.6 agreed with 7.5 obtained by tensile test at the sametemperature and in the similar stress range reduced by a knownfactor. At 180 MPa punching stress, the activation energy obtained




G Model


was 343 kJ/mol in the temperature range of 850–1050 8C. Thisactivation energy was consistent with 288–398 kJ/mol obtainedfrom uniaxial tensile tests.

Rao and Swamy [138] studied the impression creep of Ti-49 at%Al heat treated at different temperatures within the alphagamma two phase field to get 5 different volume fractions oflamellar content. Testing was done at 5 different temperaturesbetween 1023 and 1223 K and 4 levels of stress at eachtemperature. Creep rate decreased with increasing lamellarcontent. Activation energy increased linearly with lamellar contentfrom 185 kJ/mol at 22 vol% to 362 kJ/mol at 100 vol%. Stressexponent was 1.2 in all the cases.

3.16. Uranium alloys

Kutty et al. [88] studied the impression creep of the d phase ofU-50 wt%Zr alloy at 525, 550 and 575 8C. The stress exponentswere 6.90 at 525 8C between 18 and 37 MPa, 6.92 at 550 8Cbetween 15 and 28 MPa and 6.58 at 575 8C between 13 and28 MPa. The activation energy was 106 � 4 kJ/mol independent ofstress in the range of 18 and 28 MPa. This activation energy matchesthat for U diffusion in Zr for about 30 at% Zr. So climb-controlleddislocation creep is a possible mechanism.

Kutty et al. [91] used impression test to characterize the creepdeformation of U-6 wt.%Zr alloy in the temperature range of 550–650 8C in high vacuum (10�4 Torr). The punch diameter was1.5 mm, the sample thickness was 5 mm, and the maximumpenetration depth was 2.0 mm. They observed a wavy behavior ofthe impression depth at 575 8C, i.e. ‘‘negative creep’’, and suggestedthat such behavior might be due to the formation of d-phase fromthe supersaturated a-phase. Using a power relationship betweenthe punching stress and the impression velocity, they obtained thestress exponent of 3.10 at 550 8C and 8.00–8.40 for the tempera-ture in the range of 550–650 8C. The activation energy in thetemperature range of 550–650 8C is 157 � 4 kJ/mol, and the rate-controlling mechanism likely was dislocation climb.

3.17. Weldments

Hyde et al. [66] did creep tests (uniaxial, notched, impressionand cross-weld samples) on the materials of CrMoV weldmentsincluding parent materials, weld and HAZ materials in the new,service-aged, and fully repaired conditions. The creep parameterswere determined and compared.

Yu et al. [194,196] performed impression tests on high energylaser beam welds in A36 steel with constant penetration rates. Theyield strength, UTS, strain rate sensitivity, strain hardening, etc.were obtained along the fusion zone, HAZ and the base metal in theas welded condition. Impression tests seem to be the only wayobtaining such local information.

Gibbs et al. [48] made impression creep tests on an autogenousGTA aluminum weld and on an austenitic stainless steel to ferriticsteel weld. The creep resistance of the Al weld decreased from thesolidified weld metal to the base metal. The positional variationcorrelated well with the gradient of microstructure. In thedissimilar metal weldment, the minimum creep resistanceoccurred in a zone adjacent to the fusion line where creepcracking was observed to develop in service.

More work on weldments can be found in an earlier review [93].

3.18. Zircaloy

Murty et al. [122] did impression test on textured zircaloy. Theyfound along the radial, hoop and axial directions, respectively, theproportional limit was 550, 543 and 418 MPa, the yield stress was844, 866 and 804 MPa, the work hardening exponent was 0.125,


0.100 and 0.094 and the factor K was 1528, 1460 and 1305 MPa.The K is that in the equation s = Ken. They used a factor of 2.5 toconvert punching stress to uniaxial stress and divided theimpression depth by the punch diameter to obtain the uniaxialstrain.

Hussein and Murty [63] studied the effect of strain rate andtemperature on the mechanical anisotropy of zircaloy-2 TREX(tube reduced extrusion) and used both compression andimpression tests. The anisotropy seemed to disappear at hightemperatures. The yield stress ratio of about 3.15 betweenimpression and compression tests was independent of tempera-ture.

3.19. Zn alloys

Gobien et al. [49] studied Zn-4.5 wt%Al alloy prepared by ballmilling of elementary powders at cryogenic temperatures. In theas-milled condition, the volume average grain size was260 � 85 nm and after annealing at 473 K for 24 h it became510 � 173 nm. The impression creep tests at 295 K needed 72 h toreach steady state, and the creep at 373 K needed less than 24 h. Thestress dependence of impression velocity showed clearly someinternal stress or threshold stress. By using the effective stress, thestress exponent was about 1 at low stresses and 5 at high stresses. Ahyperbolic sine stress law should be tried. See a model developed byGollapudi et al. [52] and some data on nc–Zn-22 wt%Al alloy in thesection on nanocrystalline materials.

Alizadeh and Mahmudi [4] investigated the impression creep ofZn–3Cu–4Al (ZCA34), Zn–3Cu–5Al (ZCA35), and Zn–3Cu–6Al(ZCA36) solder alloys in the temperature range of 345–495 K.The punch diameter was 2.0 mm, and the sample thickness was2.5 mm. They observed that there existed an accelerated creepstage after steady state creep, and suggested that this might be dueto a phase transformation with the formation of weaker phases.Such behavior could also be due to local recrystallization, whichreduces the resistance to the creep deformation. The creep rateincreased with increasing the amount of Al in the alloy, and theyattributed this behavior to the partial spheroidisation of thelamellar eutectic structure, and the four phase transformationa + e ! T’ + h. The partial spheroidisation of the lamellar eutecticstructure reduced the resistance to the grain boundary sliding athigh temperatures. The stress exponent and activation energywere in the range of 5.0–7.9 and 52.5–100.3 kJ/mol, respectively.

3.20. Closure remarks

It is seen that impression testing is gaining popularity due to itssimplicity, the small amount of material needed and the capabilityto reach a steady state at constant load. In some situations this maybe the only test available such as the weldments or the solder ballgrid array. It is almost non-destructive so it could be used to assessthe remaining life of service.

Obviously, the impression test has many potential applications.One advantage of the impression test is that many mechanicalproperties can be characterized on a single homogeneousspecimen by taking tests at different locations. However, aftereach impression test there will be a plastic zone developedunderneath the punch and a shallow impression formed on thesurface which can create internal residual stresses inside thespecimen. If the location of the next test is too close to the firstimpression, the results may be affected by the internal stresses. Toprovide an answer to this question, finite element method needs tobe used to analyze the effect of the first impression on the newimpression tests for elastoplastic materials by varying the distancebetween these two impression tests. It is expected that a criticaldistance between two impressions can be determined.




G Model


It is known that grain boundaries are vacancy sources and sinksas well as fast paths of diffusion. Grain boundary diffusion is one ofthe rate mechanisms controlling creep of polycrystals at lowtemperatures. Using impression testing, one can measure the localeffect of grain boundary (with the punch diameter less than grainsize) and the average grain boundary effect (with the punchdiameter much larger than grain size) in the same specimen.Numerical analyses of both cases are possible to explore the effectof grain boundary on the impression deformation of polycrystals.Especially, the impression test can be used to characterize themechanical properties of nanostructured materials.

Due to the large ratio of surface area to volume, surface stress/energy plays an important role in controlling the deformationbehavior of nanostructures and localized deformation of nano-materials. The different atomic arrangement near surface fromintrinsic structure inside material leads to the formation of asurface layer likely with different mechanical properties from thecorresponding bulk phase. In general, the surface layer can deformelastoplastically, depending on the deformation rate. This willaffect the impression behavior of nanostructures. Currently, thereis no theory available to describe the elastoplastic behavior ofsurface layers. From the impression creep of nanostructures, it isexpected that one can examine the effect of surface stress/energyon the creep deformation of materials.

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